bg_hom3dex

Background due to a homogeneous spin distribution in 3D, with excluded volume

Syntax

info = bg_hom3dex()
P = bg_hom3dex(t,param)
P = bg_hom3dex(t,param,lambda)
Inputs
  • t – Time axis (N-array)
  • param – Model parameters
  • lambda – Modulation amplitude (between 0 and 1)
Outputs
  • B – Model background (N-array)
  • info – Model information (struct)

Model

../_images/model_scheme_bg_hom3dex.png

This implements a hard-shell excluded-volume model, with pumped spin concentration c (first parameter, in μM) and distance of closest approach R (second parameter, in nm).

The expression for this model is

B(t) = \mathrm{exp}\left(-\frac{8\pi^2}{9\sqrt{3}}\alpha(R) \lambda c D |t|\right)`

where c is the spin concentration (entered in spins/m3 into this expression) and D is the dipolar constant

D = \frac{\mu_0}{4\pi}\frac{(g_\mathrm{e}\mu_\mathrm{B})^2}{\hbar}

The function \alpha(R) of the exclusion distance R captures the excluded-volume effect. It is a smooth function, but doesn’t have an analytical representation. For details, see Kattnig et al, J.Phys.Chem.B 2013, 117, 16542.

Variable Symbol Default Lower bound Upper bound Description
param(1) c 50 0.01 1000 spin concentration (μM)
param(2) R 1 0.1 20 exclusion distance (nm)

Description

info = bg_hom3dex()

Returns an info structure containing the specifics of the model:

  • info.model – Full name of the parametric model.
  • info.nparam – Total number of adjustable parameters.
  • info.parameters – Structure array with information on individual parameters.
B = bg_hom3dex(t,param)

Computes the background model B from the axis t according to the parameters array param for a modulation amplitude lambda=1. The required parameters can also be found in the info structure.

B = bg_hom3dex(t,param,lambda)

Computes the background model B for a given modulation amplitude lambda (between 0 and 1).